To make a circle, you should have just 4 points. One each at 12, 3, 6 and 9 o’clock.

The same would apply to the spiral. You also want the bezier handles to adhere to a 180 or 90 degree angle (or, at the very least, keep them all at 2 consistent angles).

Vonster has a few tips on this, check out http://www.illustrationclass.com/?p=66 and download his proccess- He also recommends the http://www.logofontandlettering.com/ book

I’d follow Aluminum’s advice & redraw the whole thing, using either half circles or quarter circles, that will give you the best looking result. All it takes is a little math & a few minutes time.

hmmm... Use the spiral tool in illustrator?

i was about to mention this too i didnt really understand why you posted this question really. If your an Adobe Illustrator user like Rosem said use the spiral tool.

The spiral tool might be an easier way to draw a simple spiral, but how do you calculate what decay is required to draw your spiral, and how can you calculate the radii required (without redrawing parts of it in the first place) and then calculating what is required for the second spiral; it is simpler and quicker to redraw it from scratch using your original file as a guide.

Tim

Veerle has a tutorial about just this sort of thing.